The given mathematical expression is:

$(3 + 2) \times 4 + 10 \div (8 - 3) =$

Let's solve it step-by-step by following the order of operations (PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)):

Step 1: Simplify inside the parentheses

• $3 + 2 = 5$
• $8 - 3 = 5$

Now the expression becomes: $5 \times 4 + 10 \div 5$

Step 2: Perform multiplication and division (from left to right)

• $5 \times 4 = 20$
• $10 \div 5 = 2$

Now the expression is: $20 + 2$

Step 3: Perform addition

$20 + 2 = 22$

So, the value of the expression is:

$\boxed{22}$

Would you like more details or have any questions about this? Here are some related questions you might explore:

1. How do we prioritize multiplication and division in the order of operations?
2. What happens if the parentheses were changed in this expression?
3. How would exponents affect the result if they were added to this problem?
4. What would happen if the division came before multiplication in the original problem?
5. Could this expression be simplified further with algebraic methods?

Tip: Always remember to handle parentheses first and then follow the order of operations carefully to avoid mistakes.